This document demonstrates the use of the bRF and LASSO-D3S functions for integrative GRN inference.

Those functions infer the regulatory pathways of Arabidopsis thaliana’s roots in response to nitrate (N) induction from Varala et al., 2018.

They use as inputs the expression profiles of N-responsive genes and TFBS information. Prior TFBS information was built by searching in the promoters of the N-responsive genes the PWM of the N-responsive regulators.

Data import

Import of the expression data and the N-responsive genes and regulators :

load('rdata/inference_input_N_response_varala.rdata')
genes <- input_data$grouped_genes; length(genes)
## [1] 1426
tfs <- input_data$grouped_regressors; length(tfs)
## [1] 201
counts <- input_data$counts; dim(counts)
## [1] 1426   45
load("rdata/pwm_occurrences_N_response_varala.rdata")
dim(pwm_occurrence)
## [1] 1426  201
ALPHAS <- seq(0,1, by = 0.1)

Lauching the permutations and the true data inferences 100 times

nCores = 45
mats <- list()
nrep <- 100
for(alpha in ALPHAS){ # exploring PWM integration strength
  for(rep in 1:nrep){ # exploring inherent variability
    
    mat_rf <- bRF_inference(counts, genes, tfs, nTrees = 2000,
                            alpha = alpha,
                            pwm_occurrence = pwm_occurrence,
                            nCores = nCores,
                            importance = "%IncMSE")
    
    mat_rf_perm <- bRF_inference(counts, genes, tfs, nTrees = 2000,
                            alpha = alpha, tf_expression_permutation = TRUE,
                            pwm_occurrence = pwm_occurrence,
                            nCores = nCores,
                            importance = "%IncMSE")
    
    mats[[paste0("bRF_", as.character(alpha),  '_trueData_', rep)]] <- mat_rf
    mats[[paste0("bRF_", as.character(alpha),  '_shuffled_', rep)]] <- mat_rf_perm
    
  }
}
save(mats, file = "results/100_permutations_bRF_importances.rdata")

Thresholding the networks

load( "results/100_permutations_bRF_importances.rdata")
edges <- list()
densities <- c(0.005, 0.01,0.05,0.075)

for(name in names(mats)){ # exploring importance threshold stringency
      for(density in densities){
        edges[[paste0(name, '_', density)]] <-
        bRF_network(mats[[name]], density = density, pwm_occurrence, genes, tfs)
      }
}

save(edges, file = "results/100_permutations_bRF_edges.rdata")

names(edges)
# compure precision and recall

Thresholding the networks

load( "results/100_permutations_bRF_importances.rdata")
load("results/clusters_mse_bRF_100permutations.rdata")
positive_genes <- names(clusters_rf[clusters_rf==2])

edges <- list()
densities <- c(0.005, 0.01,0.05,0.075)

for(name in names(mats)){ # exploring importance threshold stringency
      for(density in densities){
        edges[[paste0(name, '_', density)]] <-
        bRF_network(mats[[name]][,positive_genes], density = density, pwm_occurrence, positive_genes, tfs)
      }
}

save(edges, file = "results/100_permutations_bRF_edges_positive_same_density.rdata")

# compure precision and recall

Get the postive genes their own number of edges for an equal density

color_palette = c("#C12131", "#EC5D2F", "#FE945C", "#FFC08E" )
prettyZero <- function(l){
    max.decimals = max(nchar(str_extract(l, "\\.[0-9]+")), na.rm = T)-1
    lnew = formatC(l, replace.zero = T, zero.print = "0",
        digits = max.decimals, format = "f", preserve.width=T)
    return(lnew)
}

settings <- c("method", "alpha", "dataset","rep", "density")

PWM support

load("results/100_permutations_bRF_edges.rdata")

# number of edges per network
nrows <-
  data.frame(alpha_rep = names(unlist(lapply(edges, FUN = nrow))),
             n_edges = unlist(lapply(edges, FUN = nrow)))

nrows[, settings] <-
  str_split_fixed(nrows$alpha_rep, '_', length(settings))

edges_num <- lapply(edges, function(df)
  df[sapply(df, is.numeric)])

pwm_support <-
  data.frame(alpha_rep = names(unlist(lapply(edges_num, FUN = nrow))),
             pwm = unlist(lapply(edges_num, FUN = colMeans)))
pwm_support[, settings] <-
  str_split_fixed(pwm_support$alpha_rep, '_', length(settings))

pwm_support %>%
  left_join(nrows, by = settings) %>%
  mutate(alpha = as.numeric(alpha),
         density_label = paste(density, ':', n_edges, 'edges')) %>%
  ggplot(aes(color = density_label, x = alpha, y = pwm)) +
  ggh4x::facet_nested_wrap(vars(method, density), ncol = 8, nest_line = T) +
  geom_point() +
  geom_smooth(aes(fill = density_label, linetype =dataset) , alpha = 0.1) +
  theme(
    strip.background = element_blank(),
    axis.title.x = element_text(size = 22),
    title = element_text(size = 16),
    strip.text = element_text(size = 16),
    legend.position = "top",
    legend.text = element_text(size = 15),
    axis.text = element_text(size = 12)
  ) +
  xlab(expression(alpha)) + ylab("Mean PWM score in selected edges") +
  ggtitle("Average PWM support of inferred edges") +
  guides(color = guide_legend(nrow = 2, byrow = TRUE),
         fill = guide_legend(nrow = 2, byrow = TRUE)) +
  ylab(expression(paste("mean(", pi[tr], ")"))) +
  scale_x_continuous(labels = prettyZero) +
  scale_color_manual(name = "Network density", values = color_palette) +
  scale_fill_manual(name = "Network density", values = color_palette)

## Computing validation metrics

val_conn <-
  evaluate_networks(
    edges,
    validation = c("TARGET", "CHIPSeq", "DAPSeq"),
    nCores = 15,
    input_genes = genes,
    input_tfs = tfs
  )

val_conn[, settings] <-
  str_split_fixed(val_conn$network_name, '_', length(settings))

save(val_conn, file = "results/100_permutations_bRF_validation.rdata")


val_chip <-
  evaluate_networks(
    edges,
    validation = c("CHIPSeq"),
    nCores = 15,
    input_genes = genes,
    input_tfs = tfs
  )

val_chip[, settings] <-
  str_split_fixed(val_chip$network_name, '_', length(settings))
save(val_chip, file = "results/100_permutations_bRF_validation_chip.rdata")

val_target <-
  evaluate_networks(
    edges,
    validation = c("TARGET"),
    nCores = 15,
    input_genes = genes,
    input_tfs = tfs
  )

val_target[, settings] <-
  str_split_fixed(val_target$network_name, '_', length(settings))
save(val_target, file = "results/100_permutations_bRF_validation_target.rdata")


val_dap <-
  evaluate_networks(
    edges,
    validation = c("DAPSeq"),
    nCores = 15,
    input_genes = genes,
    input_tfs = tfs
  )

val_dap[, settings] <-
  str_split_fixed(val_dap$network_name, '_', length(settings))
save(val_dap, file = "results/100_permutations_bRF_validation_dap.rdata")

Plotting validation

edges <- edges[!str_detect(names(edges), '_0.075|0.05')]



draw_precision_recall <- function(validation, data_type){
  data_val <- validation %>%
    group_by(alpha, dataset, density) %>%
    mutate(mean_precision = mean(precision, na.rm = T),
           sd_precision = sd(precision, na.rm = T),
           mean_recall = mean(recall, na.rm = T),
           sd_recall = sd(recall, na.rm = T)) %>%
  dplyr::select(-network_name) %>%
  left_join(nrows, by = settings) %>%
  mutate(alpha = as.numeric(alpha)) %>%
  mutate(density_label = paste(density, ':', n_edges, 'edges')) 

precision <- data_val %>%
    ggplot(aes(
      x = as.numeric(alpha),
      y = precision,
      color = dataset,
      fill = dataset
    ))+
    ggh4x::facet_nested_wrap(vars(method, density), ncol = 8, nest_line = T) + 
    geom_ribbon(aes(ymin = mean_precision - sd_precision , 
                    ymax = mean_precision + sd_precision  ), 
                alpha = .4)  +theme_pubr(legend = "top")+
    geom_point(alpha = 0.1) + geom_smooth(se=F)+xlab("alpha") +
  xlab(expression(alpha)) + ylab("Precision") +
  ggtitle(paste("Precision against", data_type)) +
  theme(
    strip.background = element_blank(),
    axis.title.x = element_text(size = 22),
    title = element_text(size = 16),
    strip.text = element_text(size = 16),
    legend.text = element_text(size = 15),
    axis.text = element_text(size = 12),
    legend.position = 'top'
  )

recall <- data_val%>%
    ggplot(aes(
      x = as.numeric(alpha),
      y = recall,
      color = dataset,
      fill = dataset
    ))+
    ggh4x::facet_nested_wrap(vars(method, density), ncol = 8, 
                             nest_line = T, scales = "free") + 
    geom_ribbon(aes(ymin = mean_recall - sd_recall , 
                    ymax = mean_recall + sd_recall  ), 
                alpha = .4)  +theme_pubr(legend = "none")+
    geom_point(alpha = 0.1) + geom_smooth(se=F)+xlab("alpha") +
  xlab(expression(alpha)) + ylab("Recall") +
  ggtitle(paste("Recall against", data_type)) +
  theme(
    strip.background = element_blank(),
    axis.title.x = element_text(size = 22),
    title = element_text(size = 16),
    strip.text = element_text(size = 16),
    legend.text = element_text(size = 15),
    axis.text = element_text(size = 12),
    legend.position = 'none'
  )
  return(precision/recall)
}

ConnecTF

load("results/100_permutations_bRF_validation.rdata")
draw_precision_recall(val_conn, "ConnecTF")

load(file = "results/100_permutations_bRF_validation_cluster_pos.rdata")
draw_precision_recall(val_conn_pos, "ConnecTF, positive genes")

CHIP Seq only

load("results/100_permutations_bRF_validation_chip.rdata")
draw_precision_recall(val_chip, "CHIP-Seq")

load(file = "results/100_permutations_bRF_validation_chip_cluster_pos.rdata")
draw_precision_recall(val_chip, "CHIP-Seq, positive genes")

TARGET only

load("results/100_permutations_bRF_validation_target.rdata")
draw_precision_recall(val_target, "TARGET")

load(file = "results/100_permutations_bRF_validation_target_cluster_pos.rdata")
draw_precision_recall(val_target, "TARGET, positive genes")

DAP Seq only

load("results/100_permutations_bRF_validation_dap.rdata")
draw_precision_recall(val_dap, "DAP-Seq")

load(file = "results/100_permutations_bRF_validation_dap_cluster_pos.rdata")
draw_precision_recall(val_dap, "DAP-Seq, positive genes")

How are those curves for genes from the cluster of genes with a MSE decreased significantly by data integration?

The same densities are obtained (number of edges), but after filtering edges that only point toward a group from the positive cluster of genes obtained from MSE permutations.

PWM support

load("results/100_permutations_bRF_edges_positive_same_density.rdata")
# number of edges per network
nrows <-
  data.frame(alpha_rep = names(unlist(lapply(edges, FUN = nrow))),
             n_edges = unlist(lapply(edges, FUN = nrow)))

nrows[, settings] <-
  str_split_fixed(nrows$alpha_rep, '_', length(settings))

edges_num <- lapply(edges, function(df)
  df[sapply(df, is.numeric)])

pwm_support <-
  data.frame(alpha_rep = names(unlist(lapply(edges_num, FUN = nrow))),
             pwm = unlist(lapply(edges_num, FUN = colMeans)))
pwm_support[, settings] <-
  str_split_fixed(pwm_support$alpha_rep, '_', length(settings))

pwm_support %>%
  left_join(nrows, by = settings) %>%
  mutate(alpha = as.numeric(alpha),
         density_label = paste(density, ':', n_edges, 'edges')) %>%
  ggplot(aes(color = density_label, x = alpha, y = pwm)) +
  ggh4x::facet_nested_wrap(vars(method, density), ncol = 8, nest_line = T) +
  geom_point() +
  geom_smooth(aes(fill = density_label, linetype =dataset) , alpha = 0.1) +
  theme(
    strip.background = element_blank(),
    axis.title.x = element_text(size = 22),
    title = element_text(size = 16),
    strip.text = element_text(size = 16),
    legend.position = "top",
    legend.text = element_text(size = 15),
    axis.text = element_text(size = 12)
  ) +
  xlab(expression(alpha)) + ylab("Mean PWM score in selected edges") +
  ggtitle("Average PWM support of inferred edges") +
  guides(color = guide_legend(nrow = 2, byrow = TRUE),
         fill = guide_legend(nrow = 2, byrow = TRUE)) +
  ylab(expression(paste("mean(", pi[tr], ")"))) +
  scale_x_continuous(labels = prettyZero)

Not all densities should be explored with this restriction of genes, as there are too few genes to grant sufficient interactions supported by a prior of 1. We keep only the two smallest densities.

#frees up RAM
# edges <- edges[!str_detect(names(edges), '_0.075|0.05')]
val_conn_pos <-
  evaluate_networks(
    edges,
    validation = c("TARGET", "CHIPSeq", "DAPSeq"),
    nCores = 10,
    input_genes = genes,
    input_tfs = tfs
  )


val_conn_pos[, settings] <-
  str_split_fixed(val_conn_pos$network_name, '_', length(settings))
save(val_conn_pos, file = "results/100_permutations_bRF_validation_cluster_pos.rdata")



val_chip <-
  evaluate_networks(
    edges,
    validation = c("CHIPSeq"),
    nCores = 10,
    input_genes = genes,
    input_tfs = tfs
  )

val_chip[, settings] <-
  str_split_fixed(val_chip$network_name, '_', length(settings))
save(val_chip, file = "results/100_permutations_bRF_validation_chip_cluster_pos.rdata")


val_target <-
  evaluate_networks(
    edges,
    validation = c("TARGET"),
    nCores = 10,
    input_genes = genes,
    input_tfs = tfs
  )

val_target[, settings] <-
  str_split_fixed(val_target$network_name, '_', length(settings))
save(val_target, file = "results/100_permutations_bRF_validation_target_cluster_pos.rdata")


val_dap <-
  evaluate_networks(
    edges,
    validation = c("DAPSeq"),
    nCores = 10,
    input_genes = genes,
    input_tfs = tfs
  )

val_dap[, settings] <-
  str_split_fixed(val_dap$network_name, '_', length(settings))
save(val_dap, file = "results/100_permutations_bRF_validation_dap_cluster_pos.rdata")